کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
658044 1458074 2014 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Heat or mass transfer at low Péclet number for Brinkman and Darcy flow round a sphere
موضوعات مرتبط
مهندسی و علوم پایه مهندسی شیمی جریان سیال و فرایندهای انتقال
پیش نمایش صفحه اول مقاله
Heat or mass transfer at low Péclet number for Brinkman and Darcy flow round a sphere
چکیده انگلیسی

Prior research into the effect of convection on steady-state mass transfer from a spherical particle embedded in a porous medium has used the Darcy model to describe the flow. However, a limitation of the Darcy model is that it does not account for viscous effects near boundaries. Brinkman modified the Darcy model to include these effects by introducing an extra viscous term. Here we investigate the impact of this extra viscous term on the steady-state mass transfer from a sphere at low Péclet number, Pe ≪ 1. We use singular perturbation techniques to find the approximate asymptotic solution for the concentration profile. Mass-release from the surface of the sphere is described by a Robin boundary condition, which represents a first-order chemical reaction. We find that a larger Brinkman viscous boundary layer renders mass transport by convection less effective, and reduces the asymmetry in the peri-sphere concentration profiles. We provide simple analytical expressions that can be used to calculate the concentration profiles, as well as the local and average Sherwood numbers; and comparison to numerical simulations verifies the order of magnitude of the error in the asymptotic expansions. In the appropriate limits, the asymptotic results agree with solutions previously obtained for Stokes and Darcy flow. The solution for Darcy flow with a Robin boundary condition has not been considered previously in the literature and is a new result. Whilst the article has been formulated in terms of mass transfer, the analysis is also applicable to heat transfer, with concentration replaced by temperature and the Sherwood number by the Nusselt number.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Heat and Mass Transfer - Volume 68, January 2014, Pages 247–258
نویسندگان
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